What is euclid geometry?

Answer 1

Euclid was a man - a great geometer of the ancient world. Your question should read "What is Euclidean geometry ?" The answer is : Euclidean geometry is that geometry that is based on all Euclid's axioms and postulates, including the one that says "Given a straight line on the plane and a point on the plane that is not on the line, then there can be drawn through the point and on the plane, exactly one line that never intersects the first line." Euclid knew quite well that this last was only a postulate, and that it might be possible to construct a self consistent geometry with this postulate different. It was not until the 19th century that other mathematicians caught on to this, and came up with alternative geometries. When we talk about geometries on a surface then the crucial question is whether the surface is flat - if it is then geometry is Euclidean. If the surface is curved then it isn't. Of course, we amost always do our geometry on a flat surface if we can. We can't if we are trying to navigate on the surface of the earth which is curved. The question becomes really important when we go to three dimensions; what is the geometry of space, is it curved and if so which way. The new geometries were another one of the mathematicians' pretty toys until Einstein showed us that space was in fact curved.